Abstract

The concept of $R$-diagonal element was introduced in \cite{NS2},
and was subsequently found to have applications to several problems
in free probability. In this paper we describe a new approach to
$R$-diagonality, which relies on freeness with amalgamation.
The class of $R$-diagonal elements is enlarged to contain examples
living in non-tracial $*$-probability spaces, such as the
generalized circular elements of \cite{Sh1}.